1. Field of the Invention
The present invention relates to a digital control system which performs a PID (P: Proportional, I: Integral, D: Derivative) calculation by using positional and velocity algorithms, in accordance with the characteristics of each of the terms of the PID-calculation.
2. Description of the Related Art
Controllers are classified into two categories, i.e., analog PID calculational controllers and digital PID calculational controllers. Until very recently, analog PID calculational controllers have been widely used.
An analog calculational control system performs a PID calculation by using the following PID basic equation: ##EQU1## where MV is the manipulative variable, e is deviation, K.sub.p is the proportional gain, T.sub.I is the integral action time, T.sub.D is the derivative time, and MV.sub.0 is the initial value of the manipulative variable.
Recently, digital calculational control system have come into use in increasing numbers, due to the widespread use of electronic computers and the accomplishment of high-velocity processing of signals. A digital calculational control system includes a positional algorithm system and a velocity algorithm system.
A positional algorithm system performs a PI or PID calculation during each sampling period .tau., thereby obtaining a manipulative variable MV.sub.n, where n is integer identifying the sampling period. More specifically, a PID calculational equation of the positional algorithm system can be shown by the following equation (2): ##EQU2##
A velocity algorithm system finds a change .DELTA.MV.sub.n in the MV, which occurs during each sampling period, and adds this change .DELTA.MV.sub.n to the output MV.sub.n-1 acquired in the preceding sampling period, thereby obtaining the output MV.sub.n for the sampling period. More specifically PID calculational equation of the velocity algorithm system can be represented by the following equations (3a) and (3b): ##EQU3##
The equations (2), (3a) and (3b) are obtained from the basic equation (1).
In equations (2) and (3a), e.sub.n, e.sub.n-1, and e.sub.n-2 are the deviations produced during the present sampling period, the preceding sampling period, and the sampling period preceding the preceding one, respectively. As can be understood from equation (2) with equations (3a) and (3b), the velocity algorithm system is advantageous over the positional algorithm system in the following respects:
(1). The calculation which the velocity algorithm system performs is easy since equations (3a) and (3b) have no .SIGMA.-terms.
(2) In the case of a velocity algorithm system which can be manually or automatically operated, it
suffices to control an object in accordance with MV.sub.n-1 after the manual calculation has been switched to the automatic calculation and to add .DELTA.MV.sub.n to .DELTA.MV.sub.n-1. The output obtained during the preceding sampling period, i.e., MV.sub.n-1, need not be adjusted to allow for the switching of the calculation mode. Hence, the calculation mode can be easily and smoothly changed from a manual one to an automatic one.
(3) The velocity algorithm system can accomplish a precise PID control, only if AMV.sub.n is limited, or the gain thereof is adjusted. The system is, therefore, compatible with other arithmetic calculation devices. In other words, it can easily perform calculations on not only the signals generated in itself, but also the signals processed by the other calculation devices.
For the advantages described above, most direct digital control (DDC) system in practical use are of the velocity-type.
Two conventional digital controllers, which are a positional and a velocity-type, will be described in more detail with reference to FIG. 1 and FIG. 2, respectively.
The positional PID controller shown in FIG. 1 is designed to perform the calculation according to equation (2). As FIG. 1 shows, the controller comprises a detector 1 for detecting a process variable PV.sub.n, a deviation calculator 2 for subtracting the value PV.sub.n detected by the detector 1, from a set point variable SV.sub.n, thereby calculating a deviation e.sub.n, and a positional PID calculation device 3 for performing a PID calculation according to equation (2), on the deviation e.sub.n, thereby obtaining a manipulative variable MV.sub.n. The device 3 supplies the value MV.sub.n to an object 4, thereby controlling the object 4 such that SV.sub.n becomes equal to PV.sub.n.
The velocity-type PID controller illustrated in FIG. 2 is designed to perform calculations according to equations (3a) and (3b). As FIG. 2 shows, the velocity-type PID controller comprises a detector 1 for detecting a process variable PV.sub.n, a deviation calculator 2 for subtracting the value PV.sub.n by the detector 1, from a set point variable SV.sub.n, thereby calculating a deviation en, and a velocity type PID calculation device 5 for performing a PID calculation according to equation (3a), on the deviation e.sub.n, thereby obtaining a change .DELTA.MV.sub.n in the value MV.sub.n, and a velocity-position signal converter 6 for receiving the change .DELTA.MV.sub.n and performing a calculation according to equation (3b), thus converting the change .DELTA.MV.sub.n to MV.sub.n. The converter 6 supplies the value MV.sub.n to an object 4, thereby controlling the object 4 such that SVn becomes equal to PV.sub.n. Upper and lower limits H and L of manipulative variable MV.sub.n are set to the velocity-position signal converter 6.
The positional PID digital controller (FIG. 1) is disadvantageous in some respects. Firstly, it operates at a low velocity since equation (2) includes a .SIGMA.-term. Secondly, the bumpless switching is complex, which must be carried out for the manual-automatic mode switching. Thirdly, the controller must perform complex calculations on the signals processed by the other calculating devices.
The velocity-type PID digital controller (FIG. 2) is also disadvantageous in the following respect. If the set point variable SV.sub.n is altered at time n as is shown in FIG. 3, the output value MV.sub.n must be controlled as is indicated by the broken-line curve a. If the value SV.sub.n is altered at time n, and increased over the upper limit H by value c, the output value MV.sub.n must be controlled as is indicated by the solid-line curve b, that is, the controller must perform a D calculation to reduce MV.sub.n quickly to the upper limit H. This specific control, i.e., an abrupt reduction of MV.sub.n to the upper limit H, is difficult to accomplish. Even if it is successfully achieved, it cannot apply to a boiler. Should it be used in controlling a boiler, the opening of a valve supplying air or fuel into a combustion chamber would be reduced too much, increasing the possibility of incomplete combustion and, ultimately, an explosion. The velocity-type PID controller is disadvantageous in view of stability and safety.